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Showing 1 to 20 of 33 for “"small parameter"”.
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Elliptic problems with small parameter
… boundary value problem in partial derivatives. A small parameter enters the coefficients of the main equation as well as into the boundary conditions. Such equations have already been investigated satisfactory, but there still exist certain theoretical deficiencies. Our aim is to present the …
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On the maximum number of limit cycles of certain polynomial Lienard equations
… f is a real polynomial and $\epsilon$ is a small parameter.
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The Born-Oppenheimer Approximation for Triatomic Molecules with Large Angular Momentum in Two Dimensions
… â ≤ kε<sup>-3/4</sup> for k > 0. Here the small parameter ε is the fourth root of the ratio of the electron mass to an average nuclear mass.
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The Solution of a Parabolic Partial Differential Equation via Domain Decomposition: The Synthesis of Asymptotic and Numerical Analysis
… reaction convection diffusion equation with small parameter on the diffusion term will be presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in …
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Thermonuclear Driven Fast Magnetosonic Wave Heating in Tokamak Plasmas
… geometry. We perform an expansion in the small parameter k(,(PARLL))/k(,(PERP)) of the quasi-linear diffusion coefficients. Examination of the mathematical structure of these coefficents reveals that they are independent of v(,(PARLL)) to zero order in the small parameter …
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An efficient algorithm for sensitivity analysis of chaotic systems
How does long-term chaotic behavior respond to small parameter perturbations? Using detailed models, chaotic systems are frequently simulated across disciplines – from climate science to astrophysics. But, an efficient computation of parametric derivatives of their statistics or long-term averages, …
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Analysis and Control of a Class of Stiff Linear Distributed Systems
… partial differential equations that depend on a small parameter (epsilon). First, the spectral decomposition of the so-called "stiff" operators (using the terminology of {24}) is investigated, including the convergence of their eigenvalue-eigenvector pairs as (epsilon) (--->) 0, with the …
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Numerical Methods and Their Analysis for Some Nonlinear Dispersive Equations
… to the nonrelativistic limit regime involving a small parameter \epsilon, where solutions propagate with a wavelength O(\epsilon^2) in time. Rigorous error estimates show that classical finite difference time integrators require time step to be O(\epsilon^3). A Gautschi-type integrator was …
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Bounds on edit metric codes with combinatorial DNA constraints
… provably optimal DNA codes for codes with small parameter values. And a genetic algorithm is proposed to search for some sub--optimal DNA codes with relatively large parameter values, where we can consider their sizes as reasonable lower bounds of DNA codes. Furthermore, we provide tables …
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Stability And Controls For Stochastic Dynamic Systems
… systems, which is represented by usage of a small parameter. As the small parameter goes to 0, we obtain a limit problem. Using the limit problem as a guide, we construct controls for the original problem, and show that the control so constructed is nearly optimal. In chapter 4, we revisited …
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Small and large deflection of clamped skew sandwich plates.
The problem of the small and large deflection behaviour of skew sandwich plates with built-in edges and subjected to a uniformly distributed load is investigated. Non-linear partial differential equations governing the load-displacement relationship for such plates are derived using the principle …
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On A Multi-Dimensional Singular Stochastic Control Problem: The Parabolic Case
… present approximated solutions that depend on a small parameter \epsilon > 0 and give error estimates for our regularization. These</p> <p>results extend some work on the nonlinear backward problem. Some numerical examples are given to justify the theoretical analysis.</p>
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Asymptotic analysis of vibrations of thin cylindrical shells
… the vibrations of thin shells contain several parameters, the main of which is the small parameter of the shell thickness. Formal asymptotic solutions in different domains of the space of the parameters are obtained by using a computational geometry approach. Computer algebra methods are …
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Continuum models for intergranular films in silicon nitride and comparison to atomistic simulations
… structural and electrostatic effects. A small parameter set is introduced in the model. These parameters should be adjusted based on the relation of equilibrated phase-field structures to atomistic simulations and experimental observations. To compare the continuum fields to discrete data …
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Hydrodynamic linear stability of the two-dimensional bluff-body wake through modal analysis and initial-value problem formulation
… inverse of the Reynolds number is taken as the small parameter for the multiscaling. It takes into account non-parallelism effects related to the transversal dynamics of the base flow. The first order corrections find absolute instability pockets in the first part of the intermediate wake (and …
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Travelling Wave Analysis of a Nonlinear Diffusion Equation
… a travelling wave analysis that identifies a small parameter, the natural logarithm of the compression ratio of cells at which contact inhibition stops proliferation, from which asymptotic expressions for the wave speed and proliferating rim width are derived. Subsequently, we use perturbation …
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Electromagnetic and acoustic propagation in strip lines and porous media
… and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only …
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Nonlinear transverse vibrations of centrally clamped rotating circular disks
… applications the thickness of the disk is small compared with its outer radius, we use their ratio to define a small parameter. Because the nonlinearities appearing in the governing partial-differential equations are cubic, we use the Galerkin procedure to reduce the problem into a finite …
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PRESSURE DRIVEN WALL JET FLOW NEAR CHANNEL EXIT AT MODERATE REYNOLDS NUMBER
… the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow and pressure fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface, flow in the outer layer region near …
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Two-particle level diagrammatic approaches for strongly correlated systems
… Approximation, in the process introducing a small parameter in the dual fermions perturbation theory. We demonstrate the quality of the resulting Dual Fermion DCA through a systematic study of the cluster size dependence and of the different perturbative approximations. These efforts …
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